Probability Interior Angles are Positive Integers

Date: 09/19/2001 at 17:34:12
From: Guili
Subject: Probability

My question is: Find the probability that the measure of an interior 
angle of a regular n-gon is a positive integer if n is an integer and 
3<n<12. Could you please explain? Thank you very much.

Guili

Date: 09/19/2001 at 17:47:33
From: Doctor Anthony
Subject: Re: Probability
 
 n=3 interior angle = 60    (180 - 360/3)
 n=4    "       "   = 90    (180 - 360/4)
 n=5    "       "   = 108   (180 - 360/5)  and so on

Clearly, the internal angle is an integer provided 360/n = integer.

  360/6 = 60  (integer)
  360/7      not an integer
  360/8 = 45  (integer)
  360/9 = 40  (integer)
  360/10 =36  (integer)
  360/11     not an integer
  360/12 =30  (integer)  

So, excluding 3 and 12, the internal angle will be an integer for

  n = 4, 5, 6, 8, 9, 10    (6 out of 8 occasions)

So the probability that the angle is an integer = 6/8 = 3/4.
   
- Doctor Anthony, The Math Forum
  http://mathforum.org/dr.math/   

Date: 09/19/2001 at 21:58:15
From: Guili
Subject: Re: Probability

Thank you very much for your help. I appreciate it. Now, thanks to 
you, I understand the problem.